In the world where Takahashi lives, a week has $N$ days.

Takahashi, the king of the Kingdom of AtCoder, assigns "weekday" or "holiday" to each day of week. The assignments should be the same for all weeks. At least one day of week should be assigned "holiday".

Under such conditions, the productivity of the $i$-th day of week is defined by a sequence $A$ of length $N$ as follows:

-   if the $i$-th day of week is "holiday", its productivity is $0$;
-   if the $i$-th day of week is "weekday", its productivity is $A_{\min(x,y)}$, if the last holiday is $x$ days before and the next one is $y$ days after.
    -   Note that the last/next holiday may belong to a different week due to the periodic assignments. For details, see the Samples.

Find the maximum productivity per week when the assignments are chosen optimally.  
Here, the productivity per week refers to the sum of the productivities of the $1$-st, $2$-nd, $\dots$, and $N$-th day of week.

The input is given from Standard Input in the following format:

```
$N$
$A_1$ $A_2$ $\dots$ $A_N$
```

Print the answer as an integer.

-   All values in the input are integers.
-   $1 \le N \le 5000$
-   $1 \le A_i \le 10^9$

50

For example, we can assign "holiday" to the 2-nd and 4-th day of week and "weekday" to the rest to achieve a productivity of 50 per week:

• the 1-st day of week ... x=4 and y=1, so its productivity is $A_1=10$.
• the 2-nd day of week ... it is holiday, so its productivity is 0.
• the 3-st day of week ... x=1 and y=1, so its productivity is $A_1=10$.
• the 4-th day of week ... it is holiday, so its productivity is 0.
• the 5-th day of week ... x=1 and y=4, so its productivity is $A_1=10$.
• the 6-th day of week ... x=2 and y=3, so its productivity is $A_2=10$.
• the 7-th day of week ... x=3 and y=2, so its productivity is $A_2=10$.

It is impossible to make the productivity per week 51 or greater.